An inertial reference system includes a set of inertial sensors (gyrometric sensors and accelerometric sensors) associated with processing electronics. A calculation platform, called a virtual platform PFV, then delivers the carrier speed and position information in a precise frame of reference (often denoted LGT, Local Geographic Trihedron). The virtual platform PFV allows the projection and the integration of the data arising from the inertial sensors. The inertial reference system provides information which is precise in the short term but which drifts over the long term (under the influence of the sensor defects). The control of the sensor defects represents a very significant proportion of the cost of the inertial reference system.
A satellite-based positioning receiver provides carrier position and speed information by triangulation on the basis of the signals transmitted by non-geostationary satellites visible from the carrier. The information provided may be momentarily unavailable since the receiver must have direct sight of a minimum of four satellites of the positioning system in order to be able to get location data. The information is furthermore of variable precision, dependent on the geometry of the constellation on which the triangulation is based, and noisy since it relies on the reception of signals of very low levels originating from distant satellites having a low transmission power. But they do not suffer from long-term drift, the positions of the non-geostationary satellites in their orbits being known precisely over the long term. The noise and the errors may be linked to the satellite systems, to the receiver or to the propagation of the signal between the satellite transmitter and the GNSS signals receiver. Furthermore, the satellite data may be erroneous as a consequence of faults affecting the satellites. These non-intact data must then be tagged so as not to falsify the position arising from the GNSS receiver.
To forestall satellite faults and ensure the integrity of the GNSS measurements, it is known to equip a satellite-based positioning receiver with a precision and availability estimation system termed RAIM (for “Receiver Autonomous Integrity Monitoring”) which is based on the geometry and the redundancy of the constellation of satellites used during the triangulation and on the short-term forecastable evolution of this geometry deduced from the knowledge of the trajectories of the satellites. However, the RAIM algorithm, linked purely to the satellite based locating system, is not applicable to the monitoring of location data arising from a hybrid (INS/GNSS) system and can detect only certain types of faults in a given time.
Hybridization consists in mathematically combining the position and speed information provided by the inertial reference system and the measurements provided by the satellite-based positioning receiver to obtain position and speed information taking advantage of both systems. Thus, the precision of the measurements provided by the GNSS system makes it possible to control the inertial drift and the not very noisy inertial measurements make it possible to filter the noise in the measurements of the GNSS receiver. This combination very often calls upon the Kalman filtering technique.
Kalman filtering relies on the possibilities of modeling the evolution of the state of a physical system considered in its environment, by means of an equation termed “the evolution equation” (a priori estimation), and of modeling the dependence relation existing between the states of the physical system considered and the measurements of an external sensor, by means of an equation termed “the observation equation” so as to allow readjustment of the states of the filter (a posteriori estimation). In a Kalman filter, the effective measurement or “measurement vector” makes it possible to produce an a posteriori estimate of the state of the system, which estimate is optimal in the sense that it minimizes the covariance of the error made in this estimation. The estimator part of the filter generates a posteriori estimates of the state vector of the system by using the noted deviation between the effective measurement vector and its a priori prediction so as to generate a corrective term, called an innovation. This innovation, after multiplication by a gain vector of the Kalman filter, is applied to the a priori estimate of the system state vector and leads to the obtaining of the a posteriori optimal estimate.
In the case of a hybridized INS/GNSS system, the Kalman filter receives the position and speed data provided by the inertial reference system and the positioning measurements provided by the satellite-based positioning receiver, models the evolution of the errors of the inertial reference system and delivers the a posteriori estimate of these errors which serves to correct the inertial reference system's positioning and speed data.
The estimation of the position and speed errors due to the defects of the inertial sensors appearing at the output of the virtual platform PFV of the inertial reference system is carried out by the Kalman filter. The correction of the errors by way of their estimation made by the Kalman filter can then be done at the input of the virtual platform PFV (closed-loop architecture) or at output (open-loop architecture).
When the defects of the sensors of the inertial reference system, gyrometers, accelerometers, and barometric module (one speaks in this case of a baro-inertial reference system), are not too significant, it is not necessary to apply the corrections at the input of the virtual platform PFV; the modeling of the system (linearization of the equations governing the evolution of the system), within the filter remains valid. The a posteriori estimate of the errors of the inertial reference system which is calculated in the Kalman filter is used solely for the formulation of optimal estimates of the position and speed of the carrier by deducting from the position and speed information provided by the inertial reference system its respective estimates calculated by the Kalman filter. The hybridization is then termed open loop, and in this case, the hybridization has no influence on the calculations carried out by the virtual platform PFV.
When the inertial defects are too significant or when the duration of the flight is long, the linearization of the equations governing the evolution of the inertial model integrated within the Kalman filter is no longer valid. It is therefore obligatory to apply the corrections to the virtual platform PFV so as to remain in the linear domain. The a posteriori estimate of the errors of the baro-inertial reference system which is calculated in the Kalman filter serves not only for the formulation of the optimal estimate of the position and speed of the carrier but also for the readjustment of the inertial reference system within the virtual platform PFV. The hybridization is then termed “closed loop” and the results of the hybridization filter are employed by the virtual platform to carry out its calculations.
The hybridization can also be done by observing GNSS information of different kinds. Either the carrier's position and speed, resolved by the GNSS receiver, are considered: one then speaks of loose hybridization or hybridization in geographical axes, or the information extracted upstream by the GNSS receiver is considered, namely the pseudo-distances and pseudo-speeds (quantities arising directly from the measurement of the propagation time and the Doppler effect of the signals transmitted by the satellites towards the receiver): one then speaks of tight hybridization or hybridization in satellite axes.
With a closed-loop INS/GNSS system where the location resolved by the GNSS receiver is used to readjust the information originating from the inertial reference system, it is necessary to pay particular attention to the defects affecting the information provided by the satellites since the receiver which receives them will propagate these defects to the inertial reference system, giving rise to poor readjustment of said inertial reference system. The problem arises in a particularly critical manner for ensuring the integrity of an INS/GPS hybrid location data. In what follows, we are concerned with systems integrating tight hybridization, in closed loop.
To quantify the integrity of a position measurement in applications such as aeronautical applications, where integrity is critical, a parameter called the “protection radius” of the position measurement is used. The protection radius corresponds to a maximum position error for a given probability of occurrence of error. That is to say, the probability that the position error exceeds the announced protection radius without an alarm being dispatched to a navigation system, is less than this given probability value. The calculation is based on two types of error which are on the one hand the normal measurement errors and on the other hand the errors caused by an operating anomaly of the constellation of satellites, i.e. for example a satellite fault.
The value of the protection radius of a positioning system is a key value specified by buyers wishing to purchase a positioning system. The evaluation of the value of the protection radius generally results from probability calculations using the statistical characteristics of precision of the GNSS measurements and of the behavior of the inertial sensors. These calculations are made explicit in a formal manner and allow simulations for all the cases of a GNSS constellation, for all the possible positions of the positioning system over the terrestrial globe and for all possible trajectories followed by the positioning system. The results of these simulations make it possible to provide the buyer with protection radius characteristics guaranteed by the proposed positioning system. Usually these characteristics are expressed in the form of a value of the protection radius for an availability of 100% or of a duration of unavailability for a required value of the protection radius.